Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers

Physica D: Nonlinear Phenomena

Volumn 106, Issue 1-2, 1997, Pages 167-206

  Sandstede, B ^a,c   Jones, C K R T ^a   Alexander, J C ^b  

^a BROWN UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND   (United States)

^c WIAS   (Germany)

Author keywords

Bifurcation; Homoclinic orbits; Optical fibers; Stability

Indexed keywords

ATTENUATION; BIFURCATION (MATHEMATICS); COMPUTER SIMULATION; LIGHT PROPAGATION; MATHEMATICAL MODELS; OPTICAL COMMUNICATION; OPTICAL FIBERS; STABILITY;

HOMOCLINIC ORBITS; NONLINEAR DIFFUSION MODEL; PHASE SENSITIVE AMPLIFIERS;

LASER PULSES;

EID: 0031192318     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)89488-2     Document Type: Article

References (24)

1. J.C. Alexander, R.A. Gardner and C.K.R.T. Jones, A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. 410 (1990) 167-212.
2. J.C. Alexander, M.G. Grillakis, C.K.R.T. Jones and B. Sandstede, Stability of pulses on optical fibers with phase-sensitive amplifiers, Z. Angew. Math. Phys. (1996), to appear.
3. A.R. Champneys, Subsidiary homoclinic orbits to a saddle-focus for reversible systems, Int. J. Bifurc. and Chaos 4 (1994) 1447-1482.
4. A.R. Champneys and M.D. Groves, A global investigation of solitary-wave solutions to a two-parameter model equation for water waves, Appl. Nonl. Maths., Research Report No. 2.96 (1996).
5. A.R. Champneys, Yu.A. Kuznetsov and B. Sandstede, Homcont: An auto86 driver for homoclinic bifurcation analysis, Version 2.0. Technical Report (CWI, Amsterdam, 1995).
6. A.R. Champneys, Yu.A. Kuznetsov and B. Sandstede, A numerical toolbox for homoclinic bifurcation analysis, Int. J. Bifur. and Chaos 6 (1996) 867-887.
7. E.J. Doedel and J.P. Kernévez, Auto: Software for continuation problems in ordinary differential equations with applications, Technical Report (California Institute of Technology, 1986).
8. B. Fiedler and J. Scheurle, Discretization of homoclinic orbits, rapid forcing and invisible chaos, Mem. Amer. Math. Soc. 570 (1996).
9. J. Härterich, Kaskaden homokliner Orbits in reversiblen dynamischen systemen, Diploma Thesis, University of Stuttgart (1993).
10. A. Hasegawa and Y. Kodama, Guiding-center soliton in optical fibers, Opt. Lett. 15 (1990) 1443-1445.
11. J.N. Kutz, C.V. Hile, W.L. Kath, R.-D. Li and P. Kumar, Pulse propagation in nonlinear optical fiber-lines that employ phase-sensitive parametric amplifiers, J. Opt. Soc. Am. B 11 (1994) 2112-2123.
12. J.N. Kutz and W.L. Kath, Stability of pulses in nonlinear optical fibers using phase-sensitive amplifiers, SIAM J. Appl. Math. 56 (1996) 611-626.
13. X.-B. Lin, Using Melnikov's method to solve Shilnikov's problems, Proc. Roy. Soc. Edinburgh 116 A (1990) 295-325.
14. L.F. Mollenauer, S.G. Evangelides and H. A. Haus, Long-distance soliton propagation using lumped amplifiers and dispersion shifted fiber, J. Lightwave Tech. 9 (1991) 194-197.
15. R. Remmert, Theory of Complex Functions, Graduate Texts in Mathematics, Vol. 122 (Springer, New York, 1991).
16. B. Sandstede, Verzweigungstheorie homokliner Verdopplungen, Doctoral Thesis, University of Stuttgart (1993).
17. B. Sandstede, Stability of multiple-pulse solutions, Trans. Amer. Math. Soc. (1996), to appear.
18. B. Sandstede, Instability of localised buckling modes in a one-dimensional strut model, WIAS-Preprint 247 (1996).
19. B. Sandstede, A unified approach to homoclinic bifurcations with codimension two: I. Theory (1996), in preparation.
20. B. Sandstede, Numerical computation of homoclinic flip-bifurcations (1996), in preparation.
21. M. Shub, Global Stability of Dynamical Systems (Springer, New York, 1987).
22. A. Vanderbauwhede, Subharmonic branching in reversible systems, SIAM J. Math. Anal. 21 (1990) 954-979.
23. A. Vanderbauwhede and B. Fiedler, Homoclinic period blow-up in reversible and conservative systems, Z. Angew. Math. Phys. 43 (1992) 292-318.
24. E. Yanagida, Branching of double pulse solutions from single pulse solutions in nerve axon equations, J. Differential Equations 66 (1987) 243-262.